Gas Laws - How it works
Gases vs. Solids and Liquids: A Strikingly Different Response
Regardless of the units you use, however, gases respond to changes in pressure and temperature in a remarkably different way than do solids or liquids. Using a small water sample, say, 0.2642 gal (1 l), an increase in pressure from 1-2 atm will decrease the volume of the water by less than 0.01%. A temperature increase from 32° to 212°F (0 to 100°C) will increase its volume by only 2% The response of a solid to these changes is even less dramatic; however, the reaction of air (a combination of oxygen, nitrogen, and other gases) to changes in pressure and temperature is radically different.
For air, an equivalent temperature increase would result in a volume increase of 37%, and an equivalent pressure increase will decrease the volume by a whopping 50%. Air and other gases also have a boiling point below room temperature, whereas the boiling point for water is higher than room temperature and that of solids is much higher. The reason for this striking difference in response can be explained by comparing all three forms of matter in terms of their overall structure, and in terms of their molecular behavior. (Plasma, a gas-like state found, for instance, in stars and comets' tails, does not exist on Earth, and therefore it will not be included in the comparisons that follow.)
Molecular Structure Determines Reaction
Solids possess a definite volume and a definite shape, and are relatively noncompressible: for instance, if you apply extreme pressure to a steel plate, it will bend, but not much. Liquids have a definite volume, but no definite shape, and tend to be noncompressible. Gases, on the other hand, possess no definite volume or shape, and are compressible.
At the molecular level, particles of solids tend to be definite in their arrangement and close in proximity—indeed, part of what makes a solid "solid," in the everyday meaning of that term, is the fact that its constituent parts are basically immovable. Liquid molecules, too, are close in proximity, though random in arrangement. Gas molecules, too, are random in arrangement, but tend to be more widely spaced than liquid molecules. Solid particles are slow moving, and have a strong attraction to one another, whereas gas particles are fast-moving, and have little or no attraction. (Liquids are moderate in both regards.)
Given these interesting characteristics of gases, it follows that a unique set of parameters—collectively known as the "gas laws"—are needed to describe and predict their behavior. Most of the gas laws were derived during the eighteenth and nineteenth centuries by scientists whose work is commemorated by the association of their names with the laws they discovered. These men include the English chemists Robert Boyle (1627-1691), John Dalton (1766-1844), and William Henry (1774-1836); the French physicists and chemists J. A. C. Charles (1746-1823) and Joseph Gay-Lussac (1778-1850), and the Italian physicist Amedeo Avogadro (1776-1856).
Boyle's, Charles's, and Gay-Lussac's Laws
Boyle's law holds that in isothermal conditions (that is, a situation in which temperature is kept constant), an inverse relationship exists between the volume and pressure of a gas. (An inverse relationship is a situation involving two variables, in which one of the two increases in direct proportion to the decrease in the other.) In this case, the greater the pressure, the less the volume and vice versa. Therefore the product of the volume multiplied by the pressure remains constant in all circumstances.
Charles's law also yields a constant, but in this case the temperature and volume are allowed to vary under isobarometric conditions—that is, a situation in which the pressure remains the same. As gas heats up, its volume increases, and when it cools down, its volume reduces accordingly. Hence, Charles established that the ratio of temperature to volume is constant.
By now a pattern should be emerging: both of the aforementioned laws treat one parameter (temperature in Boyle's, pressure in Charles's) as unvarying, while two other factors are treated as variables. Both in turn yield relationships between the two variables: in Boyle's law, pressure and volume are inversely related, whereas in Charles's law, temperature and volume are directly related.
In Gay-Lussac's law, a third parameter, volume, is treated as a constant, and the result is a constant ratio between the variables of pressure and temperature. According to Gay-Lussac's law, the pressure of a gas is directly related to its absolute temperature.
Absolute temperature refers to the Kelvin scale, established by William Thomson, Lord Kelvin (1824-1907). Drawing on Charles's discovery that gas at 0°C (32°F) regularly contracted by about 1/273 of its volume for every Celsius degree drop in temperature, Thomson derived the value of absolute zero (−273.15°C or −459.67°F). Using the Kelvin scale of absolute temperature, Gay-Lussac found that at lower temperatures, the pressure of a gas is lower, while at higher temperatures its pressure is higher. Thus, the ratio of pressure to temperature is a constant.
Avogadro's Law
Gay-Lussac also discovered that the ratio in which gases combine to form compounds can be expressed in whole numbers: for instance, water is composed of one part oxygen and two parts hydrogen. In the language of modern science, this would be expressed as a relationship between molecules and atoms: one molecule of water contains one oxygen atom and two hydrogen atoms.
In the early nineteenth century, however, scientists had yet to recognize a meaningful distinction between atoms and molecules. Avogadro was the first to achieve an understanding of the difference. Intrigued by the whole-number relationship discovered by Gay-Lussac, Avogadro reasoned that one liter of any gas must contain the same number of particles as a liter of another gas. He further maintained that gas consists of particles—which he called molecules—that in turn consist of one or more smaller particles.
In order to discuss the behavior of molecules, it was necessary to establish a large quantity as a basic unit, since molecules themselves are very small. For this purpose, Avogadro established the mole, a unit equal to 6.022137 × 10 23 (more than 600 billion trillion) molecules. The term "mole" can be used in the same way we use the word "dozen." Just as "a dozen" can refer to twelve cakes or twelve chickens, so "mole" always describes the same number of molecules.
Just as one liter of water, or one liter of mercury, has a certain mass, a mole of any given substance has its own particular mass, expressed in grams. The mass of one mole of iron, for instance, will always be greater than that of one mole of oxygen. The ratio between them is exactly the same as the ratio of the mass of one iron atom to one oxygen atom. Thus the mole makes if possible to compare the mass of one element or one compound to that of another.
Avogadro's law describes the connection between gas volume and number of moles. According to Avogadro's law, if the volume of gas is increased under isothermal and isobarometric conditions, the number of moles also increases. The ratio between volume and number of moles is therefore a constant.
The Ideal Gas Law
Once again, it is easy to see how Avogadro's law can be related to the laws discussed earlier, since they each involve two or more of the four parameters: temperature, pressure, volume, and quantity of molecules (that is, number of moles). In fact, all the laws so far described are brought together in what is known as the ideal gas law, sometimes called the combined gas law.
The ideal gas law can be stated as a formula, pV = nRT, where p stands for pressure, V for volume, n for number of moles, and T for temperature. R is known as the universal gas constant, a figure equal to 0.0821 atm · liter/mole · K. (Like most terms in physics, this one is best expressed in metric rather than English units.)
Given the equation pV = nRT and the fact that R is a constant, it is possible to find the value of any one variable—pressure, volume, number of moles, or temperature—as long as one knows the value of the other three. The ideal gas law also makes it possible to discern certain relations: thus if a gas is in a relatively cool state, the product of its pressure and volume is proportionately low; and if heated, its pressure and volume product increases correspondingly. Thus where p 1 V 1 is the product of its initial pressure and its initial volume, T 1 its initial temperature,
Five Postulates Regarding the Behavior of Gases
Five postulates can be applied to gases. Thesemore or less restate the terms of the earlier discussion, in which gases were compared to solidsand liquids; however, now those comparisonscan be seen in light of the gas laws.
First, the size of gas molecules is minusculein comparison to the distance between them, making gas highly compressible. In other words, there is a relatively high proportion of emptyspace between gas molecules.
Second, there is virtually no force attractinggas molecules to one another.
Third, though gas molecules move randomly, frequently colliding with one another, theirnet effect is to create uniform pressure.
Fourth, the elastic nature of the collisionsresults in no net loss of kinetic energy, the energy that an object possesses by virtue of itsmotion. If a stone is dropped from a height, it rapidly builds kinetic energy, but upon hitting anonelastic surface such as pavement, most of thatkinetic energy is transferred to the pavement. In the case of two gas molecules colliding, however, they simply bounce off one another, only to collide with other molecules and so on, with no kinetic energy lost.
Fifth, the kinetic energy of all gas molecules is directly proportional to the absolute temperature of the gas.
Laws of Partial Pressure
Two gas laws describe partial pressure. Dalton's law of partial pressure states that the total pressure of a gas is equal to the sum of its par tial pressures—that is, the pressure exerted by each component of the gas mixture. As noted earlier, air is composed mostly of nitrogen and oxygen. Along with these are small components carbon dioxide and gases collectively known as the rare or noble gases: argon, helium, krypton, neon, radon, and xenon. Hence, the total pressure of a given quantity of air is equal to the sum of the pressures exerted by each of these gases.
Henry's law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the surface of the solution. This applies only to gases such as oxygen and hydrogen that do not react chemically to liquids. On the other hand, hydrochloric acid will ionize when introduced to water: one or more of its electrons will be removed, and its atoms will convert to ions, which are either positive or negative in charge.